--- /dev/null
+/* mpfr_get_decimal64 -- convert a multiple precision floating-point number
+ to a IEEE 754r decimal64 float
+
+See http://gcc.gnu.org/ml/gcc/2006-06/msg00691.html,
+http://gcc.gnu.org/onlinedocs/gcc/Decimal-Float.html,
+and TR 24732 <http://www.open-std.org/jtc1/sc22/wg14/www/projects#24732>.
+
+Copyright 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
+Contributed by the Arenaire and Cacao projects, INRIA.
+
+This file is part of the GNU MPFR Library.
+
+The GNU MPFR Library is free software; you can redistribute it and/or modify
+it under the terms of the GNU Lesser General Public License as published by
+the Free Software Foundation; either version 2.1 of the License, or (at your
+option) any later version.
+
+The GNU MPFR Library is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
+License for more details.
+
+You should have received a copy of the GNU Lesser General Public License
+along with the GNU MPFR Library; see the file COPYING.LIB. If not, write to
+the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
+MA 02110-1301, USA. */
+
+#include <stdlib.h> /* for strtol */
+#include <string.h> /* for strcmp */
+#include "mpfr-impl.h"
+
+#define ISDIGIT(c) ('0' <= c && c <= '9')
+
+#ifdef MPFR_WANT_DECIMAL_FLOATS
+
+#ifdef DPD_FORMAT
+static int T[1000] = {
+ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 32,
+ 33, 34, 35, 36, 37, 38, 39, 40, 41, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57,
+ 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 80, 81, 82, 83, 84, 85, 86, 87, 88,
+ 89, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 112, 113, 114, 115, 116,
+ 117, 118, 119, 120, 121, 10, 11, 42, 43, 74, 75, 106, 107, 78, 79, 26, 27,
+ 58, 59, 90, 91, 122, 123, 94, 95, 128, 129, 130, 131, 132, 133, 134, 135,
+ 136, 137, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 160, 161, 162,
+ 163, 164, 165, 166, 167, 168, 169, 176, 177, 178, 179, 180, 181, 182, 183,
+ 184, 185, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 208, 209, 210,
+ 211, 212, 213, 214, 215, 216, 217, 224, 225, 226, 227, 228, 229, 230, 231,
+ 232, 233, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 138, 139, 170,
+ 171, 202, 203, 234, 235, 206, 207, 154, 155, 186, 187, 218, 219, 250, 251,
+ 222, 223, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 272, 273, 274,
+ 275, 276, 277, 278, 279, 280, 281, 288, 289, 290, 291, 292, 293, 294, 295,
+ 296, 297, 304, 305, 306, 307, 308, 309, 310, 311, 312, 313, 320, 321, 322,
+ 323, 324, 325, 326, 327, 328, 329, 336, 337, 338, 339, 340, 341, 342, 343,
+ 344, 345, 352, 353, 354, 355, 356, 357, 358, 359, 360, 361, 368, 369, 370,
+ 371, 372, 373, 374, 375, 376, 377, 266, 267, 298, 299, 330, 331, 362, 363,
+ 334, 335, 282, 283, 314, 315, 346, 347, 378, 379, 350, 351, 384, 385, 386,
+ 387, 388, 389, 390, 391, 392, 393, 400, 401, 402, 403, 404, 405, 406, 407,
+ 408, 409, 416, 417, 418, 419, 420, 421, 422, 423, 424, 425, 432, 433, 434,
+ 435, 436, 437, 438, 439, 440, 441, 448, 449, 450, 451, 452, 453, 454, 455,
+ 456, 457, 464, 465, 466, 467, 468, 469, 470, 471, 472, 473, 480, 481, 482,
+ 483, 484, 485, 486, 487, 488, 489, 496, 497, 498, 499, 500, 501, 502, 503,
+ 504, 505, 394, 395, 426, 427, 458, 459, 490, 491, 462, 463, 410, 411, 442,
+ 443, 474, 475, 506, 507, 478, 479, 512, 513, 514, 515, 516, 517, 518, 519,
+ 520, 521, 528, 529, 530, 531, 532, 533, 534, 535, 536, 537, 544, 545, 546,
+ 547, 548, 549, 550, 551, 552, 553, 560, 561, 562, 563, 564, 565, 566, 567,
+ 568, 569, 576, 577, 578, 579, 580, 581, 582, 583, 584, 585, 592, 593, 594,
+ 595, 596, 597, 598, 599, 600, 601, 608, 609, 610, 611, 612, 613, 614, 615,
+ 616, 617, 624, 625, 626, 627, 628, 629, 630, 631, 632, 633, 522, 523, 554,
+ 555, 586, 587, 618, 619, 590, 591, 538, 539, 570, 571, 602, 603, 634, 635,
+ 606, 607, 640, 641, 642, 643, 644, 645, 646, 647, 648, 649, 656, 657, 658,
+ 659, 660, 661, 662, 663, 664, 665, 672, 673, 674, 675, 676, 677, 678, 679,
+ 680, 681, 688, 689, 690, 691, 692, 693, 694, 695, 696, 697, 704, 705, 706,
+ 707, 708, 709, 710, 711, 712, 713, 720, 721, 722, 723, 724, 725, 726, 727,
+ 728, 729, 736, 737, 738, 739, 740, 741, 742, 743, 744, 745, 752, 753, 754,
+ 755, 756, 757, 758, 759, 760, 761, 650, 651, 682, 683, 714, 715, 746, 747,
+ 718, 719, 666, 667, 698, 699, 730, 731, 762, 763, 734, 735, 768, 769, 770,
+ 771, 772, 773, 774, 775, 776, 777, 784, 785, 786, 787, 788, 789, 790, 791,
+ 792, 793, 800, 801, 802, 803, 804, 805, 806, 807, 808, 809, 816, 817, 818,
+ 819, 820, 821, 822, 823, 824, 825, 832, 833, 834, 835, 836, 837, 838, 839,
+ 840, 841, 848, 849, 850, 851, 852, 853, 854, 855, 856, 857, 864, 865, 866,
+ 867, 868, 869, 870, 871, 872, 873, 880, 881, 882, 883, 884, 885, 886, 887,
+ 888, 889, 778, 779, 810, 811, 842, 843, 874, 875, 846, 847, 794, 795, 826,
+ 827, 858, 859, 890, 891, 862, 863, 896, 897, 898, 899, 900, 901, 902, 903,
+ 904, 905, 912, 913, 914, 915, 916, 917, 918, 919, 920, 921, 928, 929, 930,
+ 931, 932, 933, 934, 935, 936, 937, 944, 945, 946, 947, 948, 949, 950, 951,
+ 952, 953, 960, 961, 962, 963, 964, 965, 966, 967, 968, 969, 976, 977, 978,
+ 979, 980, 981, 982, 983, 984, 985, 992, 993, 994, 995, 996, 997, 998, 999,
+ 1000, 1001, 1008, 1009, 1010, 1011, 1012, 1013, 1014, 1015, 1016, 1017, 906,
+ 907, 938, 939, 970, 971, 1002, 1003, 974, 975, 922, 923, 954, 955, 986,
+ 987, 1018, 1019, 990, 991, 12, 13, 268, 269, 524, 525, 780, 781, 46, 47, 28,
+ 29, 284, 285, 540, 541, 796, 797, 62, 63, 44, 45, 300, 301, 556, 557, 812,
+ 813, 302, 303, 60, 61, 316, 317, 572, 573, 828, 829, 318, 319, 76, 77,
+ 332, 333, 588, 589, 844, 845, 558, 559, 92, 93, 348, 349, 604, 605, 860,
+ 861, 574, 575, 108, 109, 364, 365, 620, 621, 876, 877, 814, 815, 124, 125,
+ 380, 381, 636, 637, 892, 893, 830, 831, 14, 15, 270, 271, 526, 527, 782,
+ 783, 110, 111, 30, 31, 286, 287, 542, 543, 798, 799, 126, 127, 140, 141,
+ 396, 397, 652, 653, 908, 909, 174, 175, 156, 157, 412, 413, 668, 669, 924,
+ 925, 190, 191, 172, 173, 428, 429, 684, 685, 940, 941, 430, 431, 188, 189,
+ 444, 445, 700, 701, 956, 957, 446, 447, 204, 205, 460, 461, 716, 717, 972,
+ 973, 686, 687, 220, 221, 476, 477, 732, 733, 988, 989, 702, 703, 236, 237,
+ 492, 493, 748, 749, 1004, 1005, 942, 943, 252, 253, 508, 509, 764, 765,
+ 1020, 1021, 958, 959, 142, 143, 398, 399, 654, 655, 910, 911, 238, 239, 158,
+ 159, 414, 415, 670, 671, 926, 927, 254, 255};
+#endif
+
+/* construct a decimal64 NaN */
+static _Decimal64
+get_decimal64_nan (void)
+{
+ union ieee_double_extract x;
+ union ieee_double_decimal64 y;
+
+ x.s.exp = 1984; /* G[0]..G[4] = 11111: quiet NaN */
+ y.d = x.d;
+ return y.d64;
+}
+
+/* construct the decimal64 Inf with given sign */
+static _Decimal64
+get_decimal64_inf (int negative)
+{
+ union ieee_double_extract x;
+ union ieee_double_decimal64 y;
+
+ x.s.sig = (negative) ? 1 : 0;
+ x.s.exp = 1920; /* G[0]..G[4] = 11110: Inf */
+ y.d = x.d;
+ return y.d64;
+}
+
+/* construct the decimal64 zero with given sign */
+static _Decimal64
+get_decimal64_zero (int negative)
+{
+ union ieee_double_decimal64 y;
+
+ /* zero has the same representation in binary64 and decimal64 */
+ y.d = negative ? DBL_NEG_ZERO : 0.0;
+ return y.d64;
+}
+
+/* construct the decimal64 smallest non-zero with given sign */
+static _Decimal64
+get_decimal64_min (int negative)
+{
+ union ieee_double_extract x;
+
+ x.s.sig = (negative) ? 1 : 0;
+ x.s.exp = 0;
+ x.s.manh = 0;
+ x.s.manl = 1;
+ return x.d;
+}
+
+/* construct the decimal64 largest finite number with given sign */
+static _Decimal64
+get_decimal64_max (int negative)
+{
+ union ieee_double_extract x;
+
+ x.s.sig = (negative) ? 1 : 0;
+ x.s.exp = 1919;
+ x.s.manh = 1048575; /* 2^20-1 */
+ x.s.manl = ~0;
+ return x.d;
+}
+
+/* one-to-one conversion:
+ s is a decimal string representing a number x = m * 10^e which must be
+ exactly representable in the decimal64 format, i.e.
+ (a) the mantissa m has at most 16 decimal digits
+ (b1) -383 <= e <= 384 with m integer multiple of 10^(-15), |m| < 10
+ (b2) or -398 <= e <= 369 with m integer, |m| < 10^16.
+ Assumes s is neither NaN nor +Inf nor -Inf.
+*/
+static _Decimal64
+string_to_Decimal64 (char *s)
+{
+ long int exp = 0;
+ char m[17];
+ long n = 0; /* mantissa length */
+ char *endptr[1];
+ union ieee_double_extract x;
+ union ieee_double_decimal64 y;
+#ifdef DPD_FORMAT
+ unsigned int G, d1, d2, d3, d4, d5;
+#endif
+
+ /* read sign */
+ if (*s == '-')
+ {
+ x.s.sig = 1;
+ s ++;
+ }
+ else
+ x.s.sig = 0;
+ /* read mantissa */
+ while (ISDIGIT (*s))
+ m[n++] = *s++;
+ exp = n;
+ if (*s == '.')
+ {
+ s ++;
+ while (ISDIGIT (*s))
+ m[n++] = *s++;
+ }
+ /* we have exp digits before decimal point, and a total of n digits */
+ exp -= n; /* we will consider an integer mantissa */
+ MPFR_ASSERTN(n <= 16);
+ if (*s == 'E' || *s == 'e')
+ exp += strtol (s + 1, endptr, 10);
+ else
+ *endptr = s;
+ MPFR_ASSERTN(**endptr == '\0');
+ MPFR_ASSERTN(-398 <= exp && exp <= (long) (385 - n));
+ while (n < 16)
+ {
+ m[n++] = '0';
+ exp --;
+ }
+ /* now n=16 and -398 <= exp <= 369 */
+ m[n] = '\0';
+
+ /* compute biased exponent */
+ exp += 398;
+
+ MPFR_ASSERTN(exp >= -15);
+ if (exp < 0)
+ {
+ int i;
+ n = -exp;
+ /* check the last n digits of the mantissa are zero */
+ for (i = 1; i <= n; i++)
+ MPFR_ASSERTN(m[16 - n] == '0');
+ /* shift the first (16-n) digits to the right */
+ for (i = 16 - n - 1; i >= 0; i--)
+ m[i + n] = m[i];
+ /* zero the first n digits */
+ for (i = 0; i < n; i ++)
+ m[i] = '0';
+ exp = 0;
+ }
+
+ /* now convert to DPD or BID */
+#ifdef DPD_FORMAT
+#define CH(d) (d - '0')
+ if (m[0] >= '8')
+ G = (3 << 11) | ((exp & 768) << 1) | ((CH(m[0]) & 1) << 8);
+ else
+ G = ((exp & 768) << 3) | (CH(m[0]) << 8);
+ /* now the most 5 significant bits of G are filled */
+ G |= exp & 255;
+ d1 = T[100 * CH(m[1]) + 10 * CH(m[2]) + CH(m[3])]; /* 10-bit encoding */
+ d2 = T[100 * CH(m[4]) + 10 * CH(m[5]) + CH(m[6])]; /* 10-bit encoding */
+ d3 = T[100 * CH(m[7]) + 10 * CH(m[8]) + CH(m[9])]; /* 10-bit encoding */
+ d4 = T[100 * CH(m[10]) + 10 * CH(m[11]) + CH(m[12])]; /* 10-bit encoding */
+ d5 = T[100 * CH(m[13]) + 10 * CH(m[14]) + CH(m[15])]; /* 10-bit encoding */
+ x.s.exp = G >> 2;
+ x.s.manh = ((G & 3) << 18) | (d1 << 8) | (d2 >> 2);
+ x.s.manl = (d2 & 3) << 30;
+ x.s.manl |= (d3 << 20) | (d4 << 10) | d5;
+#else /* BID format */
+ {
+ mp_size_t rn;
+ mp_limb_t rp[2];
+ int case_i = strcmp (m, "9007199254740992") < 0;
+
+ for (n = 0; n < 16; n++)
+ m[n] -= '0';
+ rn = mpn_set_str (rp, (unsigned char *) m, 16, 10);
+ if (rn == 1)
+ rp[1] = 0;
+#if BITS_PER_MP_LIMB > 32
+ rp[1] = rp[1] << (BITS_PER_MP_LIMB - 32);
+ rp[1] |= rp[0] >> 32;
+ rp[0] &= 4294967295UL;
+#endif
+ if (case_i)
+ { /* s < 2^53: case i) */
+ x.s.exp = exp << 1;
+ x.s.manl = rp[0]; /* 32 bits */
+ x.s.manh = rp[1] & 1048575; /* 20 low bits */
+ x.s.exp |= rp[1] >> 20; /* 1 bit */
+ }
+ else /* s >= 2^53: case ii) */
+ {
+ x.s.exp = 1536 | (exp >> 1);
+ x.s.manl = rp[0];
+ x.s.manh = (rp[1] ^ 2097152) | ((exp & 1) << 19);
+ }
+ }
+#endif /* DPD_FORMAT */
+ y.d = x.d;
+ return y.d64;
+}
+
+_Decimal64
+mpfr_get_decimal64 (mpfr_srcptr src, mp_rnd_t rnd_mode)
+{
+ int negative;
+ mp_exp_t e;
+
+ /* the encoding of NaN, Inf, zero is the same under DPD or BID */
+ if (MPFR_UNLIKELY (MPFR_IS_SINGULAR (src)))
+ {
+ if (MPFR_IS_NAN (src))
+ return get_decimal64_nan ();
+
+ negative = MPFR_IS_NEG (src);
+
+ if (MPFR_IS_INF (src))
+ return get_decimal64_inf (negative);
+
+ MPFR_ASSERTD (MPFR_IS_ZERO(src));
+ return get_decimal64_zero (negative);
+ }
+
+ e = MPFR_GET_EXP (src);
+ negative = MPFR_IS_NEG (src);
+
+ /* the smallest decimal64 number is 10^(-398),
+ with 2^(-1323) < 10^(-398) < 2^(-1322) */
+ if (MPFR_UNLIKELY (e < -1323)) /* src <= 2^(-1324) < 1/2*10^(-398) */
+ {
+ if (rnd_mode == GMP_RNDZ || rnd_mode == GMP_RNDN
+ || (rnd_mode == GMP_RNDD && negative == 0)
+ || (rnd_mode == GMP_RNDU && negative != 0))
+ return get_decimal64_zero (negative);
+ else /* return the smallest non-zero number */
+ return get_decimal64_min (negative);
+ }
+ /* the largest decimal64 number is just below 10^(385) < 2^1279 */
+ else if (MPFR_UNLIKELY (e > 1279)) /* then src >= 2^1279 */
+ {
+ if (GMP_RNDZ || (rnd_mode == GMP_RNDU && negative != 0)
+ || (rnd_mode == GMP_RNDD && negative == 0))
+ return get_decimal64_max (negative);
+ else
+ return get_decimal64_inf (negative);
+ }
+ else
+ {
+ /* we need to store the sign (1), the mantissa (16), and the terminating
+ character, thus we need at least 18 characters in s */
+ char s[23];
+ mpfr_get_str (s, &e, 10, 16, src, rnd_mode);
+ /* the smallest normal number is 1.000...000E-383,
+ which corresponds to s=[0.]1000...000 and e=-382 */
+ if (e < -382)
+ {
+ /* the smallest subnormal number is 0.000...001E-383 = 1E-398,
+ which corresponds to s=[0.]1000...000 and e=-397 */
+ if (e < -397)
+ {
+ if (rnd_mode == GMP_RNDZ || rnd_mode == GMP_RNDN
+ || (rnd_mode == GMP_RNDD && negative == 0)
+ || (rnd_mode == GMP_RNDU && negative != 0))
+ return get_decimal64_zero (negative);
+ else /* return the smallest non-zero number */
+ return get_decimal64_min (negative);
+ }
+ else
+ {
+ mp_exp_t e2;
+ long digits = 16 - (-382 - e);
+ /* if e = -397 then 16 - (-382 - e) = 1 */
+ mpfr_get_str (s, &e2, 10, digits, src, rnd_mode);
+ /* Warning: we can have e2 = e + 1 here, when rounding to
+ nearest or away from zero. */
+ s[negative + digits] = 'E';
+ sprintf (s + negative + digits + 1, "%d", e2 - digits);
+ return string_to_Decimal64 (s);
+ }
+ }
+ /* the largest number is 9.999...999E+384,
+ which corresponds to s=[0.]9999...999 and e=385 */
+ else if (e > 385)
+ {
+ if (GMP_RNDZ || (rnd_mode == GMP_RNDU && negative != 0)
+ || (rnd_mode == GMP_RNDD && negative == 0))
+ return get_decimal64_max (negative);
+ else
+ return get_decimal64_inf (negative);
+ }
+ else /* -382 <= e <= 385 */
+ {
+ s[16 + negative] = 'E';
+ sprintf (s + 17 + negative, "%d", e - 16);
+ return string_to_Decimal64 (s);
+ }
+ }
+}
+
+#endif /* MPFR_WANT_DECIMAL_FLOATS */
projects / msp430-gcc.git / blobdiff